eureka math lesson 11 homework answers

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Eureka Math Student Materials: Grades K–5

Learn, Practice, Succeed

Learn, Practice, and Succeed from   Eureka Math™   offer teachers multiple ways to differentiate instruction, provide extra practice, and assess student learning. These versatile companions to   A Story of Units®   (Grades K–5) guide teachers in response to intervention (RTI), provide extra practice, and inform instruction.

Also available for Grades 6–8 . 

Learn, Practice, Succeed can be purchased all together or bundled in any configuration. Contact your account solutions manager for more information and pricing.  

The Learn book serves as a student’s in-class companion where they show their thinking, share what they know, and watch their knowledge build every day!

Application Problems:  Problem solving in a real-world context is a daily part of   Eureka Math , building student confidence and perseverance as students apply their knowledge in new and varied ways.

Problem Sets :  A carefully sequenced Problem Set provides an in-class opportunity for independent work, with multiple entry points for differentiation.

Exit Tickets:   These exercises check student understanding, providing the teacher with immediate, valuable evidence of the efficacy of that day’s instruction and informing next steps.

Templates:   Learn   includes templates for the pictures, reusable models, and data sets that students need for   Eureka Math   activities.

With   Practice , students build competence in newly acquired skills and reinforce previously learned skills in preparation for tomorrow’s lesson.   Together,   Learn   and   Practice   provide all the print materials a student uses for their core instruction.

Eureka Math  contains multiple daily opportunities to build fluency in   mathematics . Each is designed with the same notion—growing every student’s ability to use mathematics   with ease . Fluency experiences are generally fast-paced and energetic, celebrating improvement and focusing on recognizing patterns and connections within the material.

Eureka Math   fluency activities provide differentiated practice through a variety of formats—some are conducted orally, some use manipulatives, others use a personal whiteboard, or a handout and paper-and-pencil format.

Sprints:  Sprint fluency activities in  Eureka Math Practice  build speed and accuracy with already acquired skills. Used when students are nearing optimum proficiency, Sprints leverage tempo to build a low-stakes adrenaline boost that increases memory and recall. Their intentional design makes Sprints inherently differentiated – the problems build from simple to complex, with the first quadrant of problems being the simplest, and each subsequent quadrant adding complexity.

Eureka Math Succeed   enables students to work individually toward mastery.  Teachers and tutors can use  Succeed   books from prior grade levels as curriculum-consistent tools for filling gaps in foundational knowledge. Students will thrive and progress more quickly, as familiar models facilitate connections to their current, grade-level content.

Additional Problem Sets:  Ideal for Homework or extra practice, these additional problem sets align lesson-by-lesson with what is happening in the classroom. These problems are sequenced from simple-to-complex to naturally scaffold student practice. They align with   Eureka Math   and use the curriculum’s mathematical models and language, ensuring that students feel the connections and relevance to their daily instruction, whether they are working on foundational skills or getting extra practice on the current topic.

Homework Helpers:   Each problem set is accompanied by a Homework Helper, a set of worked examples that illustrate how similar problems are solved. The examples, viewed side by side with the homework, support students as they reinforce the day’s learning. Homework Helpers are also a great way to keep parents informed about math class.

Bundles and Class Sets Available

Bundle options are available for all of our materials (print, digital, PD, etc.). Prices vary by grade and size of class set. Certain grade-levels do not include all packets due to the nature of the grade-level content. Student workbooks are available in class sets of 20, 25, and 30. Prices vary by size of class set .

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3rd grade (Eureka Math/EngageNY)

Unit 1: module 1: properties of multiplication and division and solving problems with units of 2–5 and 10, unit 2: module 2: place value and problem solving with units of measure, unit 3: module 3: multiplication and division with units of 0, 1, 6–9, and multiples of 10, unit 4: module 4: multiplication and area, unit 5: module 5: fractions as numbers on the number line, unit 6: module 6: collecting and displaying data, unit 7: module 7: geometry and measurement word problems.

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Eureka Math Grade 7 Module 1 Lesson 11 Answer Key

Engage ny eureka math 7th grade module 1 lesson 11 answer key, eureka math grade 7 module 1 lesson 11 example answer key.

Example 1. Who is Faster? Answer: During their last workout, Izzy ran 2\(\frac{1}{4}\) miles in 15 minutes, and her friend Julia ran 3\(\frac{3}{4}\) miles in 25 minutes. Each girl thought she was the faster runner. Based on their last run, which girl is correct? Use any approach to find the solution.

→ We all agree that the girls ran at the same rate; however, some members of the class identified the unit rate as 9 while others gave a unit rate of \(\frac{3}{20}\) . How can both groups of students be correct? → Time can be represented in minutes; however, in real-world contexts, most people are comfortable with distance measured by hours. It is easier for a person to visualize 9 miles per hour compared to \(\frac{3}{20}\) miles per minute, although it is an acceptable answer.

→ What assumptions are made when using the formula d = rt in this problem? → We are assuming the distance is proportional to time, and that Izzy and Julia ran at a constant rate. This means they ran the same speed the entire time not slower at one point or faster at another. Picture: → Some students may decide to draw a clock. → Possible student explanation: For Izzy, every 15 minutes of running results in a distance of 2 \(\frac{1}{4}\) miles. Since the clock is divided into 15-minute intervals, I added the distance for each 15-minute interval until I reached 60 minutes. Julia’s rate is 3 \(\frac{3}{4}\) miles in 25 minutes, so I divided the clock into 25-minute intervals. Each of those 25-minute intervals represents 3 \(\frac{3}{4}\) miles. At 50 minutes, the distance represented is two times 3 \(\frac{3}{4}\) , or 7 \(\frac{1}{2}\) miles. To determine the distance ran in the last ten minutes, I needed to determine the distance for 5 minutes: 3 \(\frac{3}{4}\) ÷5 = \(\frac{3}{4}\) . Therefore, 3 \(\frac{3}{4}\) + 3 \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) = 9, or 9 miles per hour.

→ How do you find the value of a 5-minute time increment? What are you really finding? → To find the value of a 5-minute increment, you need to divide 3 \(\frac{3}{4}\) by 5 since 25 minutes is five 5-minute increments. This is finding the unit rate for a 5-minute increment. → Why were 5-minute time increments chosen? → 5-minute time increments were chosen for a few reasons. First, a clock can be separated into 5-minute intervals, so it may be easier to visualize what fractional part of an hour one has when given a 5-minute interval. Also, 5 is the greatest common factor of the two given times. → What if the times had been 24 and 32 minutes or 18 and 22 minutes? How would this affect the time increments? → If the times were 24 and 32 minutes, then the time increment would be 8-minute intervals. This is because 8 is the greatest common factor of 24 and 32. → If the times were 18 and 22 minutes, then the comparison should be broken into 2-minute intervals since the greatest common factor of 18 and 22 is 2.

→ How can we determine the unit rate? We need a denominator of 1 hour. Right now, the denominator is \(\frac{5}{6}\) hours. → We can multiply \(\frac{5}{6}\) by its multiplicative inverse \(\frac{6}{5}\) to determine a denominator of 1 hour. → Using this information, determine the unit rate in miles per hour.

Eureka Math Grade 7 Module 1 Lesson 11 Exercise Answer Key

b. Is the amount of blue paint proportional to the amount of red paint? Answer: Yes. Blue paint is proportional to red paint because there exists a constant, \(\frac{5}{3}\) =1 \(\frac{2}{3}\) , such that when each amount of red paint is multiplied by the constant, the corresponding amount of blue paint is obtained.

c. Describe, in words, what the unit rate means in the context of this problem. Answer: For every 1 \(\frac{2}{3}\) quarts of blue paint, Sally must use 1 quart of red paint.

Eureka Math Grade 7 Module 1 Lesson 11 Problem Set Answer Key

Question 1. Determine the quotient: 2 \(\frac{4}{7}\) ÷1 \(\frac{3}{6}\) . Answer: 1\(\frac{5}{7}\)

Question 2. One lap around a dirt track is \(\frac{1}{3}\) mile. It takes Bryce \(\frac{1}{9}\) hour to ride one lap. What is Bryce’s unit rate, in miles, around the track? Answer: 3

Question 3. Mr. Gengel wants to make a shelf with boards that are 1 \(\frac{1}{3}\) feet long. If he has an 18-foot board, how many pieces can he cut from the big board? Answer: 13 \(\frac{1}{2}\) boards

Question 4. The local bakery uses 1.75 cups of flour in each batch of cookies. The bakery used 5.25 cups of flour this morning. a. How many batches of cookies did the bakery make? Answer: 3 batches

b. If there are 5 dozen cookies in each batch, how many cookies did the bakery make? Answer: 5(12) = 60 There are 60 cookies per batch. 60(3) = 180 So, the bakery made 180 cookies.

Question 5. Jason eats 10 ounces of candy in 5 days. a. How many pounds does he eat per day? (Recall: 16 ounces =1 pound) Answer: \(\frac{1}{8}\) lb. each day

b. How long will it take Jason to eat 1 pound of candy? Answer: 8 days

Eureka Math Grade 7 Module 1 Lesson 11 Exit Ticket Answer Key

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